Difference between revisions of "Colloquia"

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(November 20, 2020, Reserved)
(February 8, 2021 [Mon 4-5pm], Mohamed Ndaoud (USC))
 
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<!--- in Van Vleck B239, '''unless otherwise indicated'''. --->
 
<!--- in Van Vleck B239, '''unless otherwise indicated'''. --->
  
=Fall 2020=
+
=Spring 2021=
  
== September 25, 2020, [https://www.math.tamu.edu/~jml/ Joseph Landsberg] (Texas A&M) ==
+
== January 27, 2021 '''[Wed 4-5pm]''', [https://sites.google.com/view/morganeaustern/home Morgane Austern] (Microsoft Research) ==
  
(Hosted by Gurevitch)
+
(Hosted by Roch)
 +
 
 +
'''Asymptotics of learning on dependent and structured random objects'''
 +
 
 +
Classical statistical inference relies on numerous tools from probability theory to study
 +
the properties of estimators. However, these same tools are often inadequate to study
 +
modern machine problems that frequently involve structured data (e.g networks) or
 +
complicated dependence structures (e.g dependent random matrices). In this talk, we
 +
extend universal limit theorems beyond the classical setting.
 +
 
 +
Firstly, we consider distributionally “structured” and dependent random object–i.e
 +
random objects whose distribution are invariant under the action of an amenable group.
 +
We show, under mild moment and mixing conditions, a series of universal second and
 +
third order limit theorems: central-limit theorems, concentration inequalities, Wigner
 +
semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by
 +
a series of examples in machine learning, network and information theory. Secondly
 +
by building on these results, we establish the asymptotic distribution of the cross-
 +
validated risk with the number of folds allowed to grow at an arbitrary rate. Using
 +
this, we study the statistical speed-up of cross validation compared to a train-test split
 +
procedure, which reveals surprising results even when used on simple estimators.
 +
 
 +
== January 29, 2021, [https://sites.google.com/site/isaacpurduemath/ Isaac Harris] (Purdue) ==
 +
 
 +
(Hosted by Smith)
 +
 
 +
== February 1, 2021 '''[Mon 4-5pm]''', [https://services.math.duke.edu/~nwu/index.htm Nan Wu] (Duke) ==
 +
 
 +
(Hosted by Roch)
 +
 
 +
'''From Manifold Learning to Gaussian Process Regression on Manifolds'''
 +
 
 +
In this talk, I will review the concepts in manifold learning and discuss a famous manifold learning algorithm, the Diffusion Map. I will talk about my recent research results which theoretically justify that the Diffusion Map reveals the underlying topological structure of the dataset sampled from a manifold in a high dimensional space. Moreover, I will show the application of these theoretical results in solving the regression problems on manifolds and ecological problems in real life.
 +
 
 +
== February 5, 2021, [https://hanbaeklyu.com/ Hanbaek Lyu] (UCLA) ==
 +
 
 +
(Hosted by Roch)
 +
 
 +
'''Dictionary Learning from dependent data samples and networks'''
 +
 
 +
Analyzing group behavior of systems of interacting variables is a ubiquitous problem in many fields including probability, combinatorics, and dynamical systems. This problem also naturally arises when one tries to learn essential features (dictionary atoms) from large and structured data such as networks. For instance, independently sampling some number of nodes in a sparse network hardly detects any edges between adjacent nodes. Instead, we may perform a random walk on the space of connected subgraphs, which will produce more meaningful but correlated samples. As classical results in probability were first developed for independent variables and then gradually generalized for dependent variables, many algorithms in machine learning first developed for independent data samples now need to be extended to correlated data samples. In this talk, we discuss some new results that accomplish this including some for online nonnegative matrix and tensor factorization for Markovian data. A unifying technique for handling dependence in data samples we develop is to condition on the distant past, rather than the recent history. As an application, we present a new approach for learning "basis subgraphs" from network data, that can be used for network denoising and edge inference tasks. We illustrate our method using several synthetic network models as well as Facebook, arXiv, and protein-protein interaction networks, that achieve state-of-the-art performance for such network tasks when compared to several recent methods.
  
'''From theoretic computer science to algebraic geometry: how the complexity of matrix multiplication led me to the Hilbert scheme of points.'''
+
== February 8, 2021 '''[Mon 4-5pm]''', [https://sites.google.com/view/mndaoud/home Mohamed Ndaoud] (USC) ==
  
In 1968 Strassen discovered the way we multiply nxn matrices
+
(Hosted by Roch)
(row/column)
 
is not the most efficient algorithm possible. Subsequent work has led to
 
the astounding conjecture that as the size n of the matrices grows, it
 
becomes
 
almost as easy to multiply matrices as it is to add them. I will give a
 
history
 
of this problem and explain why it is natural to study it using
 
algebraic geometry
 
and representation theory. I will conclude by discussing recent exciting
 
developments
 
that explain the second phrase in the title.
 
  
== October 9, 2020, [https://impa.br/en_US/page-pessoas/carolina-araujo/ Carolina Araujo] (IMPA)  ==
+
'''SCALED MINIMAX OPTIMALITY IN HIGH-DIMENSIONAL LINEAR REGRESSION: A NON-CONVEX ALGORITHMIC REGULARIZATION APPROACH'''
  
(Hosted by Ellenberg)
+
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies strongly on the knowledge of the true sparsity parameter s. In this paper, we present a novel fast procedure for estimation in the high dimensional linear regression. Taking advantage of the interplay between estimation, support recovery and optimization we achieve both optimal statistical accuracy and fast convergence. The main advantage of our procedure is that it is fully adaptive, making it more practical than state of the art IHT methods. Our procedure achieves optimal statistical accuracy faster than, for instance, classical algorithms for the Lasso. Moreover, we establish sharp optimal results for both estimation and support recovery. As a consequence, we present a new iterative hard thresholding algorithm for high dimensional linear regression that is scaled minimax optimal (achieves the estimation error of the oracle that knows the sparsity pattern if possible), fast and adaptive.
  
'''Symmetries in Algebraic Geometry and Cremona transformations'''
+
== February 12, 2021, [https://sites.math.washington.edu/~blwilson/ Bobby Wilson] (University of Washington) ==
  
In this talk I will discuss symmetries of complex algebraic varieties. When studying a projective variety $X$, one usually wants to understand its symmetries. Conversely, the structure of the group of automorphisms of $X$ encodes relevant geometric properties of $X$. After describing some examples of automorphism groups of projective varieties, I will discuss why the notion of automorphism is too rigid in the scope of birational geometry. We are then led to consider another class of symmetries of $X$, its birational self-maps. Birational self-maps of the projective space $\mathbb{P}^n$ are called Cremona transformations. Describing the structure of the group of Cremona transformations of the plane is a classical problem that goes back to the 19th century. In higher dimensions, not so much is known, and a natural problem is to construct interesting subgroups of the Cremona group. I will end by discussing a recent work with Alessio Corti and Alex Massarenti, where we investigate subgroups of the Cremona group consisting of symmetries preserving some special meromorphic volume forms.
+
(Hosted by Smith)
  
== October 23, 2020, [http://www.math.toronto.edu/quastel/ Jeremy Quastel] (University of Toronto) ==
+
== February 19, 2021, [http://www.mauricefabien.com/ Maurice Fabien] (Brown)==
  
(Hosted by Gorin)
+
(Hosted by Smith)
  
== November 6, 2020, [http://math.jhu.edu/~sakellar/ Yiannis Sakellaridis] (Johns Hopkins University)==
+
== February 26, 2021, [https://www.math.ias.edu/avi/home Avi Wigderson] (Princeton IAS) ==
  
 
(Hosted by Gurevitch)
 
(Hosted by Gurevitch)
  
== November 20, 2020, [https://web.ma.utexas.edu/users/ntran/ Ngoc Mai Tran] (University of Texas) ==
+
== March 12, 2021, [] ==
 +
 
 +
(Hosted by )
 +
 
 +
== March 26, 2021, [] ==
 +
 
 +
(Hosted by )
 +
 
 +
== April 9, 2021, [] ==
 +
 
 +
(Hosted by )
 +
 
 +
== April 23, 2021, [] ==
 +
 
 +
(Hosted by )
  
(Hosted by Rodriguez)
 
  
== December 4, 2020, [http://math.sfsu.edu/federico/ Federico Ardila] (San Francisco)  ==
 
  
(Hosted by Ellenberg)
 
  
 
== Past Colloquia ==
 
== Past Colloquia ==
 +
 +
[[Colloquia/Fall2020|Fall 2020]]
  
 
[[Colloquia/Spring2020|Spring 2020]]
 
[[Colloquia/Spring2020|Spring 2020]]

Latest revision as of 11:04, 20 January 2021


UW Madison mathematics Colloquium is ONLINE on Fridays at 4:00 pm.


Spring 2021

January 27, 2021 [Wed 4-5pm], Morgane Austern (Microsoft Research)

(Hosted by Roch)

Asymptotics of learning on dependent and structured random objects

Classical statistical inference relies on numerous tools from probability theory to study the properties of estimators. However, these same tools are often inadequate to study modern machine problems that frequently involve structured data (e.g networks) or complicated dependence structures (e.g dependent random matrices). In this talk, we extend universal limit theorems beyond the classical setting.

Firstly, we consider distributionally “structured” and dependent random object–i.e random objects whose distribution are invariant under the action of an amenable group. We show, under mild moment and mixing conditions, a series of universal second and third order limit theorems: central-limit theorems, concentration inequalities, Wigner semi-circular law and Berry-Esseen bounds. The utility of these will be illustrated by a series of examples in machine learning, network and information theory. Secondly by building on these results, we establish the asymptotic distribution of the cross- validated risk with the number of folds allowed to grow at an arbitrary rate. Using this, we study the statistical speed-up of cross validation compared to a train-test split procedure, which reveals surprising results even when used on simple estimators.

January 29, 2021, Isaac Harris (Purdue)

(Hosted by Smith)

February 1, 2021 [Mon 4-5pm], Nan Wu (Duke)

(Hosted by Roch)

From Manifold Learning to Gaussian Process Regression on Manifolds

In this talk, I will review the concepts in manifold learning and discuss a famous manifold learning algorithm, the Diffusion Map. I will talk about my recent research results which theoretically justify that the Diffusion Map reveals the underlying topological structure of the dataset sampled from a manifold in a high dimensional space. Moreover, I will show the application of these theoretical results in solving the regression problems on manifolds and ecological problems in real life.

February 5, 2021, Hanbaek Lyu (UCLA)

(Hosted by Roch)

Dictionary Learning from dependent data samples and networks

Analyzing group behavior of systems of interacting variables is a ubiquitous problem in many fields including probability, combinatorics, and dynamical systems. This problem also naturally arises when one tries to learn essential features (dictionary atoms) from large and structured data such as networks. For instance, independently sampling some number of nodes in a sparse network hardly detects any edges between adjacent nodes. Instead, we may perform a random walk on the space of connected subgraphs, which will produce more meaningful but correlated samples. As classical results in probability were first developed for independent variables and then gradually generalized for dependent variables, many algorithms in machine learning first developed for independent data samples now need to be extended to correlated data samples. In this talk, we discuss some new results that accomplish this including some for online nonnegative matrix and tensor factorization for Markovian data. A unifying technique for handling dependence in data samples we develop is to condition on the distant past, rather than the recent history. As an application, we present a new approach for learning "basis subgraphs" from network data, that can be used for network denoising and edge inference tasks. We illustrate our method using several synthetic network models as well as Facebook, arXiv, and protein-protein interaction networks, that achieve state-of-the-art performance for such network tasks when compared to several recent methods.

February 8, 2021 [Mon 4-5pm], Mohamed Ndaoud (USC)

(Hosted by Roch)

SCALED MINIMAX OPTIMALITY IN HIGH-DIMENSIONAL LINEAR REGRESSION: A NON-CONVEX ALGORITHMIC REGULARIZATION APPROACH

The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies strongly on the knowledge of the true sparsity parameter s. In this paper, we present a novel fast procedure for estimation in the high dimensional linear regression. Taking advantage of the interplay between estimation, support recovery and optimization we achieve both optimal statistical accuracy and fast convergence. The main advantage of our procedure is that it is fully adaptive, making it more practical than state of the art IHT methods. Our procedure achieves optimal statistical accuracy faster than, for instance, classical algorithms for the Lasso. Moreover, we establish sharp optimal results for both estimation and support recovery. As a consequence, we present a new iterative hard thresholding algorithm for high dimensional linear regression that is scaled minimax optimal (achieves the estimation error of the oracle that knows the sparsity pattern if possible), fast and adaptive.

February 12, 2021, Bobby Wilson (University of Washington)

(Hosted by Smith)

February 19, 2021, Maurice Fabien (Brown)

(Hosted by Smith)

February 26, 2021, Avi Wigderson (Princeton IAS)

(Hosted by Gurevitch)

March 12, 2021, []

(Hosted by )

March 26, 2021, []

(Hosted by )

April 9, 2021, []

(Hosted by )

April 23, 2021, []

(Hosted by )



Past Colloquia

Fall 2020

Spring 2020

Fall 2019

Spring 2019

Fall 2018

Spring 2018

Fall 2017

Spring 2017

Fall 2016

Spring 2016

Fall 2015

Spring 2015

Fall 2014

Spring 2014

Fall 2013

Spring 2013

Fall 2012

WIMAW